Mr. Pollok is certainly correct about the substantial risks you would assume in seeking to withdraw a guilty plea, by appeal or otherwise. It was my understanding from your question, however, that you did not want to do that and were attempting only to challenge the sentence.
I agree with Mr. Sachs and I apologize if I misunderstood your question.
Challenging the sentence poses a different set of questions. If the sentence is illegal, meaning the judge made a error then an appeal should be pursued if the People and the court will not correct an illegally imposed sentence on motion. If you appeal the sentence and win, there is a presumption that the judge cannot sentence you to more time on a re-sentencing and if he does, even if the greater re-sentence is legal, the People have to show that the court increased the sentence based on new aggravating facts that were not before the court on the first sentencing. Some jurisdictions place this burden of proving vindictiveness on the defendant not the prosecutor. When I win a re-sentencing, I request a remand and re-sentencing before another judge to avoid the issue but it's often not permitted.
So let's say the court initially sentenced you to two terms of 1-3 years but ran the sentences consecutively for a total 2-6 years. You take the position that running the sentences consecutively is illegal and the sentences have to run concurrently meaning three years total. So you appeal and the appellate court agrees that the sentences for the two counts have to run concurrently as a matter of law and the case is remanded for re-sentencing.
The judge then re-sentences you to two concurrent terms but of 2 1/3 to seven years which we will assume is a legal sentence. You would be able to appeal again and argue that the re-sentence was vindictive because there were no new aggravating facts that caused the court to increase the total sentence after remand.
There are also rules about challenging a sentence as unduly harsh or excessive but appellate courts in NY rarely reduce a sentence on that basis.
Lastly, there might be issues about what you were promised at the plea and whether the judge had to give you your plea back when you got a sentence you did not expect. In most federal cases, judges will give you a sentencing range and you cannot get your plea back if the sentence falls within that sentencing range. In NY, generally speaking, you get your plea back if the judge does not adhere to the promised bargained for sentence.
This is all really hypothetical and I am talking about my experiences from doing appeals in NY; I do not practice in FLorida and you need to sit down with a local lawyer in the jurisdiction and at least get a consultation. Order the plea and sentencing minutes for the lawyer to review. I hope you end up with the disposition you bargained for. There is no reason a defendant should be surprised by a sentence if they do everything that is expected of them on a plea bargain.
No worries Mr. Pollok & Thank you Joshua Sachs! Mr. Pollok thank you for the great information, I am taking notes on this. I really really appreciate your answer.